A000606 Number of nonnegative solutions to x^2 + y^2 + z^2 <= n.

1, 4, 7, 8, 11, 17, 20, 20, 23, 29, 35, 38, 39, 45, 51, 51, 54, 63, 69, 72, 78, 84, 87, 87, 90, 99, 111, 115, 115, 127, 133, 133, 136, 142, 151, 157, 163, 169, 178, 178, 184, 199, 205, 208, 211, 223, 229, 229, 230, 239, 254, 260, 266, 278, 290, 290, 296

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• H. Gupta, A Table of Values of N_3(t), Proc. National Institute of Sciences of India, 13 (1947), 35-63.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000604, A117609.

Cf. A002102 (first differences).

Programs

Mathematica

nn = 50; t = Table[0, {nn}]; Do[d = x^2 + y^2 + z^2; If[0 < d <= nn, t[[d]]++], {x, 0, nn}, {y, 0, nn}, {z, 0, nn}]; Accumulate[Join[{1}, t]] (* T. D. Noe, Apr 01 2013 *)

Python

for n in range(99):
  k = 0
  for x in range(99):
    s = x*x
    if s > n: break
    for y in range(99):
        sy = s + y*y
        if sy > n: break
        for z in range(99):
            sz = sy + z*z
            if sz > n: break
            k += 1
  print(str(k), end=',')
# Alex Ratushnyak, Apr 01 2013

Formula

G.f.: (1/(1 - x))*(Sum_{k>=0} x^(k^2))^3. - Ilya Gutkovskiy, Mar 14 2017

Extensions

More terms from Sean A. Irvine, Dec 01 2010